On infinite tensor products of projective unitary representations

TL;DR

This paper explores the theory of infinite tensor products of projective unitary representations of discrete groups, focusing on twisted regular representations, CCR-related projective representations, and their applications to product actions.

Contribution

It introduces a framework for studying infinite tensor products of projective representations, with detailed computations for free abelian groups and insights into extension problems.

Findings

Analysis of infinite tensor products for specific group classes

Explicit computations for free abelian groups

Insights into extension problems for product actions

Abstract

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with CCR-representations of bilinear maps. Detailed computations are presented in the case where G is a finitely generated free abelian group. We also discuss an extension problem about product type actions of G, where the projective representation theory of G plays a central role.